Semiclassical Theory of Chaotic Conductors

TL;DR

This paper develops a semiclassical theory to calculate the Landauer conductance in chaotic ballistic devices, accounting for all orders in the inverse number of channels, and reveals how trajectory self-encounters influence conductance.

Contribution

It introduces a comprehensive semiclassical framework for conductance in chaotic systems, extending previous approaches to all orders in inverse channel number and including magnetic field effects.

Findings

Families of trajectory pairs contribute similarly to periodic orbit pairs.

Close self-encounters slightly hinder trajectory escape into leads.

The theory applies to chaotic ballistic devices with and without magnetic fields.

Abstract

We calculate the Landauer conductance through chaotic ballistic devices in the semiclassical limit, to all orders in the inverse number of scattering channels without and with a magnetic field. Families of pairs of entrance-to-exit trajectories contribute, similarly to the pairs of periodic orbits making up the small-time expansion of the spectral form factor of chaotic dynamics. As a clue to the exact result we find that close self-encounters slightly hinder the escape of trajectories into leads.